# Radius of Convergence of the Power Series

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Complex Variable

Radius of Convergence of the Power Series

âˆž âˆž

Theorem:- âˆ‘ anzn is a power series and âˆ‘ nanzn - 1 is the power series obtained

n=0 n=0

by differentiating the first series term by term.

Then the derived series has the same radius of convergence as the original series.

See the attached file.

Â© BrainMass Inc. brainmass.com October 6, 2022, 2:09 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/radius-convergence-power-series-37243

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Complex Variable

Radius of Convergence of the Power Series

âˆž âˆž

Theorem:- âˆ‘ anzn is a power series and âˆ‘ nanzn - 1 is the power series obtained

n=0 n=0

by differentiating the first series term by term.

Then the derived series has the same radius of convergence as the original series.

See the attached file for the solution of the problem.

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Â© BrainMass Inc. brainmass.com October 6, 2022, 2:09 pm ad1c9bdddf>https://brainmass.com/math/basic-algebra/radius-convergence-power-series-37243